DE 10 2004 033 545 A1 discloses a burner using a fuel cell which is used in a fuel cell system for combustion of residual gases, i.e., anode exhaust gas and cathode exhaust gas. The burner comprises a combustion chamber bordered at the inlet end by a supply wall and at the output end by a heat exchanger. The combustion chamber is also encompassed laterally by a burner wall. The supply wall has a burner zone with oxidizer gas openings to supply the combustion chamber with oxidizer gas and with combustion gas openings to supply the combustion chamber with combustion gas. With the known burner, an inside wall encompassing the combustion chamber laterally is arranged inside the burner wall and at a distance therefrom to provide thermal insulation for the combustion chamber. This creates an annular cooling space, which is supplied with gaseous coolant, between the inside wall and the burner wall on the outside. The gaseous coolant is supplied through openings in the supply wall. Oxidizer gas supplied to the oxidizer gas openings of the burner zone is preferably used as the gaseous coolant.